Resumen de A method for simulating the influence of grain boundaries and material interfaces on electromigration
Continued scaling of the back-end-of-line copper metalization has shown to significantly increase the resistivity and decrease the lifetime of interconnects. The primary reason is the impact of microstructure, meaning the influence of grain boundaries and material interfaces on the movement of conducting electrons and atoms during electromigration. Modeling this phenomenon is especially challenging since the boundaries and interfaces must be treated independently from the grain bulk. Usually, this results in an extremely fine mesh with very high computational and memory requirements. In this manuscript, we present an efficient approach to treat grain boundaries and material interfaces when modeling electromigration in copper nano-interconnects. Our approach uses several spatial material parameters to identify the locations of the grain boundaries and material interfaces during a simulation, thereby not requiring the definition of multiple materials or complex meshes and geometrical interfaces. Using this method even very coarse meshes, with grid spacings twice the size of the thinnest element (the grain boundary thickness), were able to reasonably reproduce the vacancy concentration of thin copper interconnects, including their microstructure. Furthermore, we were able to calculate the stress build-up at triple points with high accuracy even when using a very coarse mesh.
